Observation of the long-term variability of Cygnus X-1
with MAXI
Juri Sugimoto,1,2 Shunji Kitamoto,2 Tatehiro Mihara1 and the MAXI team
1MAXI team, Institute of Physical and Chemical Research (RIKEN), 2-1 Hirosawa, Wako, Saitama 351-0198, Japan2
Department of Physics, Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo 171-8501, Japan
E-mail(JS): sugimoto@crab.riken.jp
A BSTRACTWe studied the long-term X-ray variability of the black hole binary, Cygnus X-1, using about
6 years of MAXI data from 2009 to 2016, in the high/soft state (HSS) and the low/hard state(LHS). We analyzed an aperiodic long-term variation, using Normalized Power Spectrum Densities (NPSDs), in the frequency range from 10−7 to 10−4 Hz, with 2 − 4 keV, 4 − 10 keV and
10 − 20 keV data. From the comparison with previous works in the frequency region above
10−3 Hz, it was shown that the NPSD extends with a single index from 10−3 to 10−7 Hz in boththe LHS and HSS. Such the long-term variation is mostly caused by the power-law component
in the energy spectrum. In the LHS, the variability slightly decreased towards higher energies,
while in the HSS, the variability was found to increase significantly with energy. To explain ourresults of the long-term aperiodic variation, we propose a new large-scale disk structure. In ourmodel, an optically-thin and geometrically-thick accretion flow coexists with an optically-thickand geometrically-thin, standard accretion disk, which is extending up to a large radius of ∼ 1012
cm, in both HSS and LHS.
K EY WORDS : black hole physics — accretion, accretion disks—X-ray:general — stars: individual: Cygnus X-1

1. Introduction
In the X-ray universe, a mass accretion is seen invarious phenomena. Among them an accretion disk
is commonly formed around a compact star in an
X-ray binary system. Such a compact star shines releasing the gravitational energy of the accreting gas
from the companion star. The X-ray binary, especially with a black hole (BH), is studied by a lot ofresearchers, focusing on the accretion disk, including the accretion flow.
An important information obtained from observations is a time variation of the X-ray intensity. Infact, the typical BH binary, Cygnus X-1 (Cyg X1), is drawn attention to its violent time-variation
since its discovery in 1960’s. It has an irregular andlarge-amplitude variation in the range of 0.1 ∼ afew second. The cause of the time variation is related with the characteristics of the accretion flow in
the accretion disk, especially within 10 rS (rS is theSchwarzschild radius) where majority of X-rays areemitted.
On the other hand, the long-term variation morethan 1000 s is not well understood. Because most ofobservations are made by X-ray telescopes mounted
on the satellites orbiting a low Earth orbit. Such atime variation in the scale of several tens of days
is important to understand the complete structure of
the accretion disk. In order to investigate the overall structure of the accretion disk, especially of Cyg
X-1, we studied aperiodic long-term variation of theintensity. We use the X-ray data obtained by MAXI
which provides us a statistically good X-ray intensity and a spectrum every 90-minite spaning morethan six years.
2. Observation
We analyzed the data of Cyg X-1 obtained withMAXI (Matsuoka et al. 2009). We downloaded
archival data of Cyg X-1 of one-day bin and 90-

minute bin from the MAXI home page1 .
Figure 1 showed one-day bin light curves of Cyg
X-1 obtained with the GSC from 2009 August 15(MJD = 55058) to 2016 January 30 (MJD = 57417),
in three energy bands (2 − 4 keV, 4 − 10 keV and10 − 20 keV). A time history of the hardness ratio(HR), I(4 − 10 keV) / I(2 − 4 keV), is also plotted.
The state of Cyg X-1 can be recognized by the values of the HR as the HSS (HR<0.43) and the LHS(HR>0.48).
Since the start of the MAXI observation in 2009
August, Cyg X-1 was in the LHS for about tenmonths. At around MJD = 55378, the source madea transition to the HSS, where it stayed for anotherten months. After several times of state transitions,
it has been mainly in the HSS since MJD = 56078.
3. Analysis
3.1. Definition of NPSDs
The X-ray light curve with 90-minute bin was converted to the PSD by the discrete Fourier transformation as,Fc (f ) =2 ∑yj cos(2πf ∆t × j),
N j=1

Fs (f ) =2 ∑yj sin(2πf ∆t × j),
N j=1
N(1)

where yi is the intensity (photons s−1 cm−2 ) at thei-th bin, N is the number of data after filling thegaps as described in Sugimoto et al. (2016), and∆t is a time interval of 5400 s, which is the regular sampling time of the MAXI public data, f is
the frequency which is an integer multiple of ∆f = T1
and T is the total time span of the observation. Thefactor of 2/N is employed so that Fc (f ) and Fs (f )represent the amplitude of the cosine and sine components, respectively, regardless of N . The power,1222 (Fc (f ) + Fs (f )), is that in the frequency range∆f . Therefore the PSD, power per Hz, is,}1 { 2Fc (f ) + Fs2 (f ) .
2∆fTo obtain the real NPSD from the MAXI data
two corrections are necessary; the gap correction
and the aliasing correction. The MAXI data are notcompletely regular-sampled. Sometimes data gaps
are caused by sun avoidance, high particle background regions, small dead regions around the scanpoles which move with the precession period of theorbit of the ISS, and other effects. Furthermore,MAXI measurements are snapshots. It scans an Xray source only for 40 ∼ 70 s, every 5400 s period. Each data point is a very short snapshot, witha long interval to the next sampling. As a result, aMAXI data point contains source variations not only
on time scale longer than 5400 s, but also to these inbetween 40 ∼ 70 s and ∼ 5400 s. We described theestimation of these effects and derived a “transferfunction” for the calculated PSD to the best estimation of the real PSD in Sugimoto et al. (2016).

3.2. Long-term PSDs v.s. short-term PSDsN

P (f ) =average intensity following Miyamoto et al. (1994).
It is called an Normalized PSD (NPSD).

(2)

The unit is (RMS2 /Hz). To represent relative amplitude, the PSD is normalized by the square of the*1 http://maxi.riken.jp/top/index.php?cid=1&jname=J1958+352

Although we can make a long-term PSD by using
all the 6years of data, single PSD is difficult to estimate the errors of data points. We shorten the data
length to 40 and 43 days for the LHS and the HSS,
respectively, calculated NPSDs, and averaged them.
The errors of NPSDs obtained in this way can be expected statistically and have smaller errors. Instead,it lacks the information in the lowest frequencies.
The data span covers a frequency range down to ∼3×10−7 Hz. Six data segments were extracted for
the LHS, and eight data segments for the HSS. Then,
we converted these data segments individually into
NPSDs, and took their averages over the LHS andHSS separately.
Figure 2 shows our 4 − 10 keV NPSDs in bothstates, in comparison with previous works withRXTE data by Cui et al. (1997), Pottschmidt et al.
(2003), and Reig et al. (2002). In both states, our results at 10−4 Hz locate on simple extrapolations of
the NPSDs obtained previously by the RXTE/PCA
in the frequency region above 10−3 Hz. The NPSD
in Reig et al. (2002), which is obtained by theRXTE/ASM, is located between the two states ofthe present work. This difference is presumably because their data included some of the HSS and thetransition periods, although the main part was in theLHS.

2-4 keV

X-ray intensity(photons s-1 cm-2 )

420
1.5
10.5
0

4-10 keV

10-20 keV

0.4
0.2
0

(4-10 keV)/(2-4 keV)

10.5055200

2010

55400

55600

2011

55800

56000

56200

2012

56400

2013

56600

56800

2014

57000

57200

2015

57400 (MJD)

2016 (year)

Fig. 1. One-day bin light curves and HR histories of Cyg X-1 obtained with the MAXI/GSC. From the top to bottom panels,
the 2 − 4 keV, 4 − 10 keV and 10 − 20 keV intensities, and the hardness ratio, I(4 − 10 keV) / I(2 − 4 keV), are plotted.
The blue and red regions indicate the LHS and the HSS periods, respectively. Data points with large error bars, due
to high background counts, were omitted.

3.3.

Energy dependence of the long-term
NPSD in the HSS
The long-term NPSD in the HSS was obtained forthe first time. Figure 3 shows the NPSD in theHSS in the frequency range of 3 hours to 1 month.
The vertical error bars represent the NPSD scattering (standard deviation) within each ensemble. We
found that the high-energy bands (4 − 10 keV and10 − 20 keV), which correspond to the power law
component in the energy spectrum, are more variable than the low energy band (2 − 4 keV), whichcorresponds to the disk component. It means thatthe power law component is responsible for the observed long-term intensity variations, while the disk
emission is essentially constant.
4. Discussion
The short-term variation above 10−3 Hz is thoughtto reflect the phenomena occurring in the vicinityof the BH. On the other hand, it is unlikely that thelong-term variation in the range of 10−7 Hz is generated there. We consider that it is generated at alarge radius and propagates inwards as a variationof the mass accretion rate. Then most of the X-rays
are radiated from the vicinity of the BH. Here, wediscuss that how the long-term variation is propagated to the vicinity of the BH. The time scales ofthe variation newly produced in the accretion disk
are the dynamical time scale, td , and thermal timescale, tth , expressed as
td = Ω−1K ,tth = (αΩK )−1 .

(3)

On the other hand, the time scale of the accretionis the viscous time scale of the accretion disk, tvis ,expressed astvis = (αΩK )−1(Hr)−2.

(4)

We compared these time scales in the standard
disk and in the RIAF. In an optically-thick andgeometrically-thin standard disk, the thickness ofthe disk H is much smaller than the radius r. Then,the viscous time scale is larger than the other twotime scales, and variations produced at any outerradii would be strongly dissipated and would notpropagate down to the X-ray emitting region. On theother hand, in an optically-thin and geometricallythick flow (RIAF), H is the same level as r. In thiscase the thermal time scale is of the same order as
the viscous time scale, and the fluctuations can propagate inwards, varying the X-ray intensity on a wide
range of time scales.
Then, we proposed a new large-scale accretion disk structure as illustrated in figure 4. The
optically-thin flow (RIAF) should co-exist from thevicinity of the BH to the radius of ∼ 1012 cm.

References
Churazov, E. et al. 2001, MNRAS., 321, 759
Cui, W. et al. 1997, Transparent Universe, 382, 209
Matsuoka, M. et al. 2009, PASJ, 61, 999
Mihara, T. et al. 2011, PASJ, 63, 623
Miyamoto, S. et al. 1994, ApJ, 435, 398
Pottschmidt, K. et al. 2003, A&A, 407, 1039
Reig, P. et al. 2002, A&A, 383, 202
Sugimoto, J. et al. 2016, PASJ, 68, S17
Tomida, H. et al. 2011, PASJ, 63, 397

105

Reig+2002

103HSSLHS110Cui+1997

10-1
Pottschmidt+2003-3

1010-8

10-6

100
10-2
10-4
frequency (Hz)102

Fig. 2. A comparison of the MAXI 4 − 10 keV NPSDs in theLHS (blue) and the HSS (red), with the previous works.
The dashed line is the 2 − 13 keV NPSD in the LHSby Pottschmidt et al. (2003), the dotted line is that inthe HSS in 2 − 13 keV by Cui et al. (1997), and the
dot-dashed line is that by Reig et al. (2002), where themost data are in the LHS.

105

NPSD

5. Conclusion
Using six years archival data obtained with MAXI,
we derived the NPSDs of Cyg X-1 in its LHS and
HSS from 10−7 Hz to 10−4 Hz in the three energy
bands. It is paticularly important that the long-term
variations in the two states were studied in a unified
way using the same instrument, with the same analysis method, and under similar data statistics. The
PSD of the both states in the frequency range between 10−5 and 10−4 Hz were also provided by ourwork for the first time. Our results in both states
were approximated by a power law, and on an extrapolation of the NPSD previously obtained in frequencies above 10−4 Hz.
Also the long-term NPSD in the HSS was obtained for the first time. The NPSD from 10−7 Hz
to 10−4 Hz in the HSS depends on energy in sucha way that it is 5∼6 times higher in the 10 − 20
keV band than that in the low energy band (2 − 4keV). This result is expected to provide some clues
to the still unknown origin of the hard-tail component, which is nearly always observed in the HSS.
We then proposed a new disk structure. Theoptically-thin corona should extend to ∼ 1012 cm,
and a standard optically-thick and geometricallythin disk co-exists in the out side of the certain radius. The long-term variation produced at the large
radius is transported to the vicinity of the compact
star, via the optically-thin corona, and eventually Xray intensity of the power law component shows thelong-term variation.

NPSD

The long-term variation produced at the large radius is transported to the vicinity of the compact
star, via the RIAF, and eventually X-ray intensity ofthe power law component shows the long-term variation.

104103
102
101

month

10-7

weekday

10-6
10-5Frequency (Hz)10-4

Fig. 3. The NPSDs calculated over data segments (43 d ×
8 for the HSS), and averaged.

X-ray emitting region

RIAF
BH

standard disk~1012 cm

Fig. 4. Illustration of our accretion model.